Question: Solve for $b$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $30b+53 \geq 18b -83$
Answer: $\begin{aligned}30b+53 & \geq 18b -83 \\\\ 30b&\geq 18b-136 &(\text{Subtract } 53 \text{ from both sides}) \\\\ 12b &\geq -136 &(\text{Subtract } 18b \text{ from both sides})\\\\ b&\geq-\dfrac{34}{3}&(\text{Divide both sides by }12 \text{ and simplify}) \end{aligned}$ In conclusion, the answer is $b \geq -\dfrac{34}{3}$.